Recently, hypergraphs have attracted a lot of attention due to their ability to capture complex relations among entities. The insurgence of hypergraphs has resulted in data of increasing size and complexity that exhibit interesting small-scale and local structure, e.g., small-scale communities and localized node-ranking around a given set of seed nodes. Popular and principled ways to capture the local structure are the local hypergraph clustering problem and the related seed set expansion problem. In this work, we propose the first local diffusion method that achieves edge-sizeindependent Cheeger-type guarantee for the problem of local hypergraph clustering while applying to a rich class of higher-order relations that covers a number of previously studied special cases.

Sign stochastic gradient descent (signSGD) is a communication-efficient method that transmits only the sign of stochastic gradients for parameter updating.

Score distillation sampling (SDS) has proven to be an important tool, enabling the use of large-scale diffusion priors for tasks operating in data-poor domains. Unfortunately, SDS has a number of characteristic artifacts that limit its usefulness in general-purpose applications. In this paper, we make progress toward understanding the behavior of SDS and its variants by viewing them as solving an optimal-cost transport path from a source distribution to a target distribution. Under this new interpretation, these methods seek to transport corrupted images (source) to the natural image distribution (target). We argue that current methods' characteristic artifacts are caused by (1) linear approximation of the optimal path and (2) poor estimates of the source distribution. We show that calibrating the text conditioning of the source distribution can produce high-quality generation and translation results with little extra overhead. Our method can be easily applied across many domains, matching or beating the performance of specialized methods. We demonstrate its utility in text-to-2D, text-based NeRF optimization, translating paintings to real images, optical illusion generation, and 3D sketch-to-real. We compare our method to existing approaches for score distillation sampling and show that it can produce high-frequency details with realistic colors.

Since their initial introduction, score-based diffusion models (SDMs) have been successfully applied to solve a variety of linear inverse problems in finite-dimensional vector spaces due to their ability to efficiently approximate the posterior distribution. However, using SDMs for inverse problems in infinite-dimensional function spaces has only been addressed recently, primarily through methods that learn the unconditional score. While this approach is advantageous for some inverse problems, it is mostly heuristic and involves numerous computationally costly forward operator evaluations during posterior sampling. To address these limitations, we propose a theoretically grounded method for sampling from the posterior of infinite-dimensional Bayesian linear inverse problems based on amortized conditional SDMs. In particular, we prove that one of the most successful approaches for estimating the conditional score in finite dimensions--the conditional denoising estimator--can also be applied in infinite dimensions. A significant part of our analysis is dedicated to demonstrating that extending infinite-dimensional SDMs to the conditional setting requires careful consideration, as the conditional score typically blows up for small times, contrarily to the unconditional score. We conclude by presenting stylized and large-scale numerical examples that validate our approach, offer additional insights, and demonstrate that our method enables large-scale, discretization-invariant Bayesian inference.

Social bias in machine learning has drawn significant attention, with work ranging from demonstrations of bias in a multitude of applications, curating definitions of fairness for different contexts, to developing algorithms to mitigate bias. In natural language processing, gender bias has been shown to exist in context-free word embeddings. Recently, contextual word representations have outperformed word embeddings in several downstream NLP tasks. These word representations are conditioned on their context within a sentence, and can also be used to encode the entire sentence. In this paper, we analyze the extent to which state-of-the-art models for contextual word representations, such as BERT and GPT-2, encode biases with respect to gender, race, and intersectional identities. Towards this, we propose assessing bias at the contextual word level. This novel approach captures the contextual effects of bias missing in context-free word embeddings, yet avoids confounding effects that underestimate bias at the sentence encoding level. We demonstrate evidence of bias at the corpus level, find varying evidence of bias in embedding association tests, show in particular that racial bias is strongly encoded in contextual word models, and observe that bias effects for intersectional minorities are exacerbated beyond their constituent minority identities. Further, evaluating bias effects at the contextual word level captures biases that are not captured at the sentence level, confirming the need for our novel approach.

The last two cases correspond to cost function gradients perpendicular to the faces of the feasible region. In linear optimization, these cases give is an infinite number of optimal solutions between two adjacent vertices. B.1 Baseline Algorithms We provide a brief discussion of the baseline algorithms below. The libraries our implementations are based off for PPO, SAC, and DreamerV2 are available under the MIT License, and the base MPO implementation under the Apache License 2.0. For MuJoCo [52], we used a Pro Lab license.

Unlike the prior results on fast spherical harmonic transform, our proposed algorithm works efficiently using a nearly optimal number of samples in any dimension d. Furthermore, we illustrate the empirical performance of our algorithm on numerical examples.

Neural operators effectively solve PDE problems from data without knowing the explicit equations, which learn the map from the input sequences of observed samples to the predicted values. Most existing works build the model in the original geometric space, leading to high computational costs when the number of sample points is large. We present the Latent Neural Operator (LNO) solving PDEs in the latent space. In particular, we first propose Physics-Cross-Attention (PhCA) transforming representation from the geometric space to the latent space, then learn the operator in the latent space, and finally recover the real-world geometric space via the inverse PhCA map. Our model retains flexibility that can decode values in any position not limited to locations defined in the training set, and therefore can naturally perform interpolation and extrapolation tasks particularly useful for inverse problems. Moreover, the proposed LNO improves both prediction accuracy and computational efficiency. Experiments show that LNO reduces the GPU memory by 50%, speeds up training 1.8 times, and reaches state-of-the-art accuracy on four out of six benchmarks for forward problems and a benchmark for inverse problem.

Unpaired image-to-image translation aims to translate an input image to another domain such that the output image looks like an image from another domain while important semantic information are preserved. Inferring the optimal mapping with unpaired data is impossible without making any assumptions. In this paper, we make a density changing assumption where image patches of high probability density should be mapped to patches of high probability density in another domain. Then we propose an efficient way to enforce this assumption: we train the flows as density estimators and penalize the variance of density changes. Despite its simplicity, our method achieves the best performance on benchmark datasets and needs only 56 86% of training time of the existing state-of-the-art method. The training and evaluation code are avaliable at https://github.com/Mid-Push/

This paper identifies a structural property of data distributions that enables deep neural networks to learn hierarchically. We define the "staircase" property for functions over the Boolean hypercube, which posits that high-order Fourier coefficients are reachable from lower-order Fourier coefficients along increasing chains. We prove that functions satisfying this property can be learned in polynomial time using layerwise stochastic coordinate descent on regular neural networks - a class of network architectures and initializations that have homogeneity properties. Our analysis shows that for such staircase functions and neural networks, the gradient-based algorithm learns high-level features by greedily combining lower-level features along the depth of the network. We further back our theoretical results with experiments showing that staircase functions are learnable by more standard ResNet architectures with stochastic gradient descent. Both the theoretical and experimental results support the fact that the staircase property has a role to play in understanding the capabilities of gradient-based learning on regular networks, in contrast to general polynomial-size networks that can emulate any Statistical Query or PAC algorithm, as recently shown.